Depends who you talk to.
I'm sure some people reckon the cylinders can get a glaze on em by running engine in. One example was a bike team who fitted a brand bew engine athen raced it. Dyno before and after, it made 15bhp more after the race. Dunno what it would have made if it was run in?

IMHO for a small outboard - its probably as much about having the chance to run the engine and so flush out any dirt/swarf in the gearbox / sump oil. the advice I got when running mine in was - get it up on the plane as quickly as possible then throttle back to keep it there - and keep changing the throttle. It was suggested that labouring the engine by running it 1/2 on the plane would be worse for it than getting it over the hump. Did make any difference? who knows - like 99% of people I have not had any cause to dismantle the engine to see what state its in - but it runs fine! I was surprised how much fine metal was in the gearbox oil after 10 hrs (been fine since).

Part of my job involves audio and video equipment, and believe it or not we are told to "run in" both high end speakers and high end flat panels.

The reasoning is that once you get the kit up to normal operating temperature, keeping it there for a while allows the various components to reach their settled position, and thereafter you get better performance because you have reached the 'comfort zone' for the kit.

Whether this gives us 0.01% better performance I'm not able to definitely quote on, but the proposition makes sense to me - and given that a lot of failures of all sorts of things are due to fluctuations in temperature - I was quite happy to follow the running in guidelines if this allows the various bits of the outboard to 'bed in' at their normal operating temperatures in low-stress situations.

So, sorry, no hard and fast physics, just a vague feeling that new bits of metal getting warm and cold should be treated a bit gingerly for the first few hours.

I used to have motorbikes and there was endless discussion about how to run engines in. Some said flat out from the start would give more power, others that you should vary the speeds and be careful for 1,000 miles.
The conclusions from the bike racing fraternity was that an engine thrashed from new will deliver more power, but not last as long. An engine run in by the book won't deliver as much power, but will last longer.
There was also some discussion about oil. Some said mineral oil was best for "running in" as it allowed the parts to "bed in". Using top quality synthetic oil was no good as it protected the parts too well, and they did not bed in properly!

Not running in an engine will ultimately give you a noisier, rattlier and leakier engine - perhaps a little faster. Treating with care for the first 1,000 miles in a car or 10 hours or so on a marine engine should mean additional long-term performance. The engine designers recommend running in, they have their reasons.

I've had a few cars over the years of differing sizes including a few 6L V12's, I've run them all in gently and have been rewarded with tighter happier engines.